Principles Determining the Structure of Transition Metals

For the better part of a century researchers across disciplines have sought to explain the crystallography of the elemental transition metals: hexagonal close packed, body centered cubic, and face centered cubic in a form similar to that used to rationalize the structure of organic molecules and inorganic complexes. Pauling himself tried with limited success to address the origins of transition metal stability. These early investigators were handicapped, however, by incomplete knowledge regarding the structure of metallic electron density. Here, we exploit modern approaches to electron density analysis to first comprehensively describe transition metal electron density. Then, we use topological partitioning and quantum mechanically rigorous treatments of kinetic energy to account for the structure of the density as arising from the interactions between metallic polyhedra. We argue that the crystallography of the early transition metals results from charge transfer from the so called “octahedral” to “tetrahedral cages” while the face centered cubic structure of the late transition metals is a consequence of anti-bonding interactions that increase octahedral hole kinetic energy.     

Improving the Catalytic Performance of the Hydrogen Evolution Reaction of α-MoB2 via Rational Doping by Transition Metal Elements

Abundant transition metal borides are emerging as promising electrochemical hydrogen evolution reaction (HER) catalysts which have a potential to substitute noble metals. Those containing graphene-like (flat) boron layers, such as α-MoB2, are particularly promising and their performance can be further enhanced via doping by the second metal. In order to understand intrinsic effect of doping and rationalize selection of dopants, we employ density functional theory (DFT) calculations to study substitutional doping of α-MoB₂ by transition metals as a route towards systematic improvement of intrinsic catalytic activity towards HER. We calculated thermodynamic stability of various transition metal elements to select metals which form a stable ternary phase with α-MoB₂. We inspected surface stability of dopants and assessed catalytic activity of doped surface through hydrogen binding free energy at various hydrogen coverages. We calculated the reaction barriers and pathways for the Tafel step of HER for the most promising dopants. The results highlight iron as the best dopant, simultaneously lowering the reaction barrier of the Tafel step while having suitable thermodynamic stability within MoB₂ lattice.     

Dupré–Blundell model for the Landau diamagnetism applied to electrons gyrating in a crystalline solid

The model developed by Dupré and Blundell for calculating the Landau diamagnetism of free electrons is adapted to the case when the tightly bound electrons in a crystal lattice are submitted to the action of the magnetic field. In particular, the frequency of the electron gyration and the energy change contributing to the nonoscillating part of the diamagnetism are considered for the simple cubic and the body‐centered cubic lattices. The plots of the energy change done versus the position of the Fermi energy in a crystal exhibit much different behavior than a similar plot obtained in the free‐electron case. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2009     

Structural stability analysis of Wigner crystal with Gaussian and Yukawa‐type positive background

Calculations of the ground‐state energies of Wigner crystals having simple cubic (sc), body‐centered cubic (bcc), face‐centered cubic (fcc), diamond, and perovskite structures and (hence) the analysis of relative stability of Wigner crystals of various different structures are reported. The positive background is represented by a periodic array of Gaussians and Yukawa‐type distribution. The effects on stability of the perturbation due to the underlying lattice have been demonstrated. Among the structures, the bcc lattice still remains the most stable known arrangement and the Yukawa‐type background leads to a lower ground state energy value compared to a Gaussian type. The calculations are done for the range of the density parameter r_s corresponding to low densities for the above two cases. The range of low‐density region favorable for Wigner crystallization is found to be above r_s=20. The role of correlation energy is suitably taken into account. © 2001 John Wiley & Sons, Inc. Int J Quantum Chem, 2001     

Survival probabilities in three-dimensional random walks

We evaluate the survival probability for random walkers on lattices doped with traps. We consider nearest-neighborstep walks and walks mediated bi multipolar interactions, for which the probability of steps of length r is proportional to r^?s. The decay law due to trapping is calculated for the diamond, simple cubic and body- and face-centered cubic lattices. We establish validity domains of approximate expressions.     

Nitrogen-doped mesoporous carbon nanospheres loaded with cobalt nanoparticles for oxygen reduction and Zn–air batteries

Mesoporous carbon supported with transition metals nanoparticles performs desired activities for oxygen reduction reaction (ORR) and clean energy conversion devices such as Zn–air batteries. In this work, we synthesized N-doped mesoporous carbon loaded with cobalt nanoparticles (CoMCN) through self-assembly method. There are sufficient mesopores on the carbon substrate which stem from the pore-forming agent. These mesopores can provide enough accessible active sites and profitable charge/mass transport for ORR. The high content of pyridinic and graphitic N is beneficial for promoting O₂ adsorption and reduction. The smaller value of I_D/I_G indicates the higher degree of graphitization of CoMCN, providing better electronic conductivity. The half-wave potential of CoMCN is 0.865 V in basic solution, which is 24 mV more positive than that of the commercial Pt/C (0.841 V). In addition, CoMCN performs excellent methanol tolerance and stability under both basic and acidic conditions. The Zn–air battery assembled with CoMCN performs the larger power density and open-circuit voltage than the commercial Pt/C-based battery, indicating the potential application in energy conversion systems. This work provides thoughtful ideas for fabricating transition metal nanoparticles based porous carbon for electrocatalysis and metal–air batteries.     

A Computational Study of 3‐D Helium Clusters

Physical and thermodynamic properties have been calculated and analyzed for the best and optimized geometries of the 3‐D clusters with N = 3 to N = 10 atoms and unit cells of three types of crystalline systems using ab initio RHF/6–31G^** method. Dependence of the lattice binding energy on the cluster parameter, R, has been studied. Similar behavior observed for the binding energies for all clusters shows that probabilities of their existence in the condensed phase are more or less the same. In the next step, thermodynamic properties have been calculated and analyzed for He₂₇ 3‐D helium clusters with simple cubic, body centered cubic (bcc), trigonal and hexagonal (hcp) configurations. The results show that the hexagonal cluster is more favored over other clusters. It is found that these clusters are electronically stable over a limited range of the values for the lattice parameter. Δ_fH is constant in this stability region and thus the Δ_fG exactly follows the variations of TΔ_fS. Surface effects have been investigated by comparing the square and hexagonal He₉ 2‐D lattices with the cubic and hexagonal He₂₇ 3‐D lattices, respectively. The lattice parameters, densities and molar volumes calculated for the clusters with hcp and bcc configurations have satisfactory agreement with the available experimental values. Properties of the He₁₃, He₃₄ and He₁₀₄ hcp clusters have also been calculated and analyzed.     

Simple metal and binary alloy phases based on the hcp structure: Electronic origin of distortions and superlattices

Crystal structures of simple metals and binary alloy phases based on the close-packed hexagonal (hcp) structure are analyzed within the model of Fermi sphere – Brillouin zone interactions to understand distortions and superlattices. Examination of the Brillouin-Jones configuration in relation to the nearly-free electron Fermi sphere for several representative phases reveals significance of the electron energy contribution to the phase stability. This approach may be useful for understanding high pressure structures recently found in compressed simple alkali and alkali-earth metals.     

Stable clusters in the condensed state and some possibilities for gas phase clusters

The classical naked cluster ions of the post-transition elements that are stable in solid compounds and their lower charged analogues observed in mixed metal beams reflect the reduced number of good bonding orbitals. New cluster ions of indium that are hypoelectronic (fewer than 2n+2 skeletal bonding electrons) because of distortions or the bonding of heterometal atoms within the clusters are described. A large family of new, orbital-rich clusters of the group III and IV transition metals sheathed by halide are all centered by a wide variety of heteroatoms. Factors in their stability, possible analogous naked cluster targets, and some calculations are considered.     

The Hückel model for small metal clusters. IV. Orbital properties and cohesive energies for model clusters of up to several hundred atoms

We examine model cluster structures by applying the simple Hückel method to spherically symmetric clusters whose atoms are constrained to occupy cubic (simple, body centered, or face-centered) and hop lattice positions. The Hückel orbitals are organized into energy supershells, many of which remain well separated even at 500–600 atom cluster sizes. The classical droplet model provides a good fit to cluster atomization energies, which then correctly extrapolate to the bulk cohesive energy predicted by tight-binding calculations. Energy level distributions for cubic lattices show that features characteristic of a tight-binding solid become fully evident in clusters containing as few as 100 atoms. A particular example is the high density of states found for the Fermi level of bcc clusters, vestiges of which might suffice to confer on suitable materials an enhanced electrical conductivity.     

Magnetoresistance effect,Runge–Lenz vector,and the torque vector due to anisotropy of electron orbits in cubic lattices submitted to the action of a constant magnetic field

Parameters due to an anisotropic character of the electron orbits in cubic metals submitted to the action of an external magnetic field are calculated. These parameters are, in the first step, a nonzero value of the metal magnetoresistance and—in the second step—the nonvanishing electron torque vector and the Runge–Lenz vector. Both these vectors depend on the electron angular momentum in the crystal lattices, which is also examined together with the radius of curvature of the electron orbits. The calculation of magnetoresistance is specified to the case of the body‐centered cubic lattice of metallic iron for which a comparison of the theory with the experimental data for magnetoresistance is also presented. © 2002 Wiley Periodicals, Inc. Int J Quantum Chem, 2002     

On the lattice stability of metals

A tight-binding calculation for body-centred cubic (bcc) and face-centred cubic (fcc) lithium is carried out using muffin-tin potentials which differ only in the arrangement of the muffin-tin spheres. The essential results are not restricted to lithium but also hold for other metals with similar s-p-bands. The bcc structure can be stable for the lowest valence states. The stability of fcc increases with increasing valence electron concentration. This is due to the kinetic energy which behaves as in an empty lattice case. In accordance with the behaviour of the kinetic energy, the lowest energy states have the highest distribution probability between neighbouring atoms. They are mostly delocalized. The trend in the lattice stability is explained in terms of the differences in the packing of the lattices. In real cases where the virial theorem holds an appropriate part of the kinetic energy is changed into potential energy. Hybridization plays a completely different role from that in covalent compounds. It stabilizes a compound by delocalizing the charge density.     

Hydrides with the perovskite structure: General bonding and stability considerations and the new representative CaNiH3

The stability and electronic structure of perovskite hydrides ABH₃ were investigated by means of first-principles density functional calculations. Two types of perovskite hydrides are distinguished: (1) When A and B are alkali and alkaline earth metals, the hydrides are ionic compounds with calculated band gaps of around 2 eV and higher. Their stability trend follows basically the concept of Goldschmidt's tolerance factor. (2) When A is one of the heavier alkaline earth metals (Ca, Sr, Ba) and B a transition metal, stable compounds ABH₃ result only when B is from the Fe, Co, or Ni groups. This stability trend is basically determined by effects associated with d band filling of both the transition metal and the hydride. In contrast to group (1) perovskites, the transition metal-containing compounds are metals. The synthesis of CaNiH₃ and its structure determination from CaNiD₃ is reported. This compound is a type (2) perovskite hydride with a fully occupied hydrogen position (CaNiD₃: a=3.551(4) Å, d_Ni-D=1.776(2) Å). Its stability is discussed with respect to transition metal hydrides with complex anions (e.g., Mg₂NiH₄, Na₂PdH₂, Sr₂PdH₄).     

Kinetics of phase transition and thermal stability in Se80?x Te20Zn x (x?=?2, 4, 6, 8, and 10) glasses

Se_80?x Te₂₀Zn _x (x?=?2, 4, 6, 8, and 10) glasses have been prepared using conventional melt quenching technique. The kinetics of phase transformations (glass transition and crystallization) have been studied using differential scanning calorimetry (DSC) under non-isothermal condition at five different heating rates in these glasses. The activation energy of glass transition (E _t), activation energy of crystallization (E _c), Avrami exponent (n), dimensionality of growth (m), and frequency factor (K _o) have been investigated for the better understanding of growth mechanism using different theoretical models. The activation energy is found to be highly dependent on Zn concentration. The rate of crystallization is found to be lowest for Se₇₀Te₂₀Zn₁₀ glassy alloy. The thermal stability of these glasses has been investigated using various stability parameters. The values of these parameters were obtained using characteristic temperatures, such as glass transition temperature T _g, onset crystallization temperature T _c, and peak crystallization temperature T _p. In addition to this, enthalpy-released during crystallization has also been determined. The values of stability parameters show that the thermal stability increases with the increase in Zn concentration in the investigated glassy samples.     

Incorporation of transition metals into Mg-Al layered double hydroxides: Coprecipitation of cations vs. their pre-complexation with an anionic chelator

A comparative study on two different methods for preparing Mg-Al layered double hydroxides (LDH) containing various divalent transition metals M (M=Co, Ni, Cu) has been carried out. The first (conventional) method involved coprecipitation of divalent metals M(II) with Mg(II) and Al(III) cations using carbonate under basic conditions. The second approach was based on the ability of transition metals to form stable anionic chelates with edta⁴⁻ (edta⁴⁻=ethylenediaminetetraacetate) that were synthesized and further introduced into LDH by coprecipitation with Mg and Al. The synthesized LDHs were characterized by X-ray diffraction (XRD) and X-ray fluorescence (XRF) methods, thermogravimetry with mass-selective detection of decomposition products (TG-MSD), Fourier transform infrared (FTIR) and Raman spectroscopy techniques. The results obtained were discussed in terms of efficiency of transition metal incorporation into the LDH structure, thermal stability of materials and the ability of metal chelates to intercalate the interlayer space of Mg-Al LDH. Vibrational spectroscopy studies confirmed that the integrity of the metal chelates was preserved upon incorporation into the LDH.     

Next-nearest neighbour contributions to P 2p3/2 X-ray photoelectron binding energy shifts of mixed transition-metal phosphides M1−xM′xP with the MnP-type structure

X-ray photoelectron (XPS) and X-ray absorption (XANES) spectroscopic measurements have been made for several series of mixed transition-metal phosphides M_1−xM′_xP (Co_1−xMn_xP, Mn_1−xV_xP, and Co_1−xV_xP), which adopt the MnP-type structure (M is more electronegative than M′). The P 2p binding energy shifts displayed by the mixed metal phosphide members do not follow the trend shown by the simple binary phosphides, a deviation which arises from the contribution of next-nearest neighbour effects operating on the primary photoemission site. The magnitude of this contribution can be derived from a simple charge potential model taking the metal electronegativity differences into account. It is suggested that these next-nearest neighbour contributions induce a charge transfer between the two dissimilar metals via metal-metal bonding, which modifies the Madelung potential experienced at the photoemission site. This charge transfer has been confirmed by analysis of the Co 2p XPS spectra as well as the P and Mn K-edge XANES spectra.     

Potassium under pressure: Electronic origin of complex structures

Recent high-pressure X-ray diffraction studies of alkali metals revealed unusual complex structures that follow the body-centred and face-centred cubic structures on compression. The structural sequence of potassium under compression to 1 Mbar is as follows: bcc–fcc–h-g (tI19*), hP4–oP8–tI4–oC16.We consider configurations of Brillouin-Jones zones and the Fermi surface within a nearly-free-electron model in order to analyze the importance of these configurations for the crystal structure stability. Formation of Brillouin zone planes close to the Fermi surface is related to opening an energy gap at these planes and reduction of crystal energy. Under pressure, this mechanism becomes more important leading to appearance of complex low-symmetry structures. The stability of the post-fcc phases in K is attributed to the changes in the valence electron configuration under strong compression.     

Incompletely symmetric non-bloch electron states in perfect cubic crystals. I. Eigenproblem and its solution

In the studies on impure metals where the perturbation potential due to the impurity has symmetry of the point group of the crystal, subdivision of the electron density of the pure metal into irreducible representations of the point group is of significance. A method is presented for the calculation of wave functions of the perfect cubic crystal which transform according to the incompletely symmetric irreducible representations of the point group. The functions were evaluated in the LCAO approximation using s-type AOS for the face centered cubic lattice. These are in the form of standing waves, and their coefficient functions are linear combinations of the products of the cubic harmonics of a suitable type and the spherical Bessel functions. Properties of the solutions obtained were examined. Numerical calculations were made for four irreducible representations of the point group.     

Gas-phase reactions of doubly charged alkaline earth and transition metal complexes of acetonitrile, pyridine, and methanol generated by electrospray ionization

Formation and low energy collision-induced dissociation (CID) of doubly charged metal(II) complexes ([metal(II)+L _n ]²⁺, metal(II)=Co(II), Mn(II), Ca(II), Sr(II) and L = acetonitrile, pyridine, and methanol) were investigated. Complexes of [metal(II)+L _n ]²⁺ where n≤7 were obtained using electrospray ionization. Experimental parameters controlling the dissociation pathways for [Co(II)+(CH₃CN)₂]²⁺ were studied and a strong dependence of these processes on the collision energy was found. However, the dissociation pathways appear to be independent of the cone potential, indicating low internal energy of the precursor ions. In order to probe how these processes are related to intrinsic parameters of the ligand such as ionization potential and metal ion coordination, low energy CID spectra of [metal(II)+L _n ]²⁺ for ligands such as acetonitrile, pyridine, and methanol were compared. For L = pyridine, all metals including the alkaline earth metals Ca and Sr were reduced to the bare [metal(I)]⁺ species. Hydride transfer was detected upon low energy CID of [metal(II)+L _n ]²⁺ for metal(II)=Co(II) and Mn(II) and L = methanol, and corroborated by signals for [metal(II)+H^?]⁺ and [metal(II)+H^?+CH₃OH]⁺, as well as by the complementary ion [CH₃O]⁺.     

Nobler than the Noblest: Noncubic Gold Microcrystallites

Conventional gold comprising the cubic lattice is universally known for its stability. However, well known to chemists and metallurgists, this nobility is challenged by reagents such as aqua regia, which dissolve gold to form a salt solution. Among metals, mercury blends with gold to form amalgam, otherwise transition metals such as copper tend to interact with gold surfaces in electrochemical media. Herein, we report a combined experimental and theoretical investigation of the stability of Au microcrystallites bearing unconventional crystal lattices that exhibit enhanced stability towards Hg and aqua regia and practically no interaction with Cu during electroless plating. The unconventional gold is undoubtedly nobler.